Andreotti-Grauert theory by integral formulas:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
1988
|
| Series: | Progress in mathematics
74 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 270 S. |
| ISBN: | 3764334134 0817634134 |
Staff View
MARC
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| 100 | 1 | |a Chenkin, Gennadij M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Andreotti-Grauert theory by integral formulas |c Gennadi M. Henkin ; Jürgen Leiterer |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1988 | |
| 300 | |a 270 S. | ||
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Record in the Search Index
| _version_ | 1804115686562201600 |
|---|---|
| adam_text | CONTENTS
CHAPTER I. INTEGRAL FORMULAS AND FIRST APPLICATIONS 9
Summary 9
0. Generalities about differential forms and currents 9
1. The Martinelli-Bochner-Koppelman formula and the Kodaira finite-
ness theorem 21
2. Cauchy-Fantappie formulas, the Poineare 5-lemma, the Dolbeault
isomorphism and smoothing of the 5-cohomology 34
3. Piecewise Cauchy-Fantappie formulas 46
CHAPTER II. q-CONVEX AND q-CONCAVE MANIFOLDS 59
Summary 59
4. q-convex functions 59
5. q-convex manifolds 65
6. q-concave functions and q-concave manifolds 73
CHAPTER III. THE CAOCHY-RIEMANN EQUATION ON q-CONVEX MANIFOLDS 77
Summary 77
7. Local solution of 5u=f- on strictly q-convex domains with
r n-q 78
8. Local approximation of 5-closed (0,n-q-l)-forms on strictly
q-convex domains 83
9. Uniform estimates for the local solutions of the 5-equation
constructed in Sect. 7 86
10. Local uniform approximation of 5-closed (0,n-q-1)-forms on
strictly q-convex domains 93
11. Finiteness of the Dolbeault cohomolotfy of order r with uniform
estimates on strictly q-convex domains with r n-q 96
12. Global uniform approximation of 3-closed (0,n-q-l)-forms and
invariance of the Dolbeault cohomology of order n-q with respect
to q-convex extensions, and the Andreotti-Grauert finiteness
theorem for the Dolbeault cohomology of order n-q on q-convex
manifolds 100
7
CHAPTER IV. THE CAUCHY-RIEMANN EQUATION ON q-CONCAVE MANIFOLDS 117
Summary 117
13. Local solution of 5u=fQ on strictly q-concave domains with
Kr q-1, and the local Hartogs extension phenomenon 118
14. Uniform estimates for the local solutions of the d-equation
obtained in Sect. 13, and finiteness of the Dolbeault cohomo¬
logy of order r with uniform estimates on strictly q-convave
domains with l r q-l 128
15. Invarianoe of the Dolbeault cohomology of order 0 r q-l with
respect to q-concave extensions, and the Andreotti-Grauert
finiteness theorem for the Dolbeault cohomology of order 0 r q-l
on q-concave manifolds 135
16. A uniqueness theorem for the Dolbeault cohomology of order q
with respect to q-concave extensions 144
17. The Martineau theorem on the representation of the Dolbeault
cohomology of a concave domain by the space of holomorphic
functions on the dual domain 146
18. Solution of the E.Levi problem for the Dolbeault cohomology: the
Andreotti-Norguet theorem on infiniteness of the Dolbeault coho¬
mology of order q on q-concave - (n-q-1)-convex manifolds 156
19. The Andreotti-Vesentini separation theorem for the Dolbeault
cohomology of order q on q-concave manifolds 164
CHAPTER V. SOME APPLICATIONS 197
20. Solvability oriterions for 5u=f and duality between the
Dolbeault cohomology with compact support and the usual
Dolbeault cohomology 197
21. The domain |z°|2+...+|zq|2 |zq+1I2+...+|znl2 210
22. The condition Z(r) 211
23. The Rossi theorem on attaching complex manifolds to a complex
manifold along a strictly pseudoconcave boundary of real
dimension 5 213
24. Rossi s example of a real 3-dimensional strictly pseudoconcave
boundary which cannot be embedded into CN 216
NOTES 220
PROBLEMS 226
APPENDIX A. Estimation of some integrals (the smooth case) 232
APPENDIX B. Estimation of some integrals (the non-smooth case) 241
BIBLIOGRAPHY 262
LIST OF SYMBOLS 268
SUBJECT INDEX 270
8
|
| any_adam_object | 1 |
| author | Chenkin, Gennadij M. Leiterer, Jürgen 1945- |
| author_GND | (DE-588)1047631776 |
| author_facet | Chenkin, Gennadij M. Leiterer, Jürgen 1945- |
| author_role | aut aut |
| author_sort | Chenkin, Gennadij M. |
| author_variant | g m c gm gmc j l jl |
| building | Verbundindex |
| bvnumber | BV001294829 |
| classification_rvk | SK 780 |
| classification_tum | MAT 322f |
| ctrlnum | (OCoLC)242685916 (DE-599)BVBBV001294829 |
| dewey-full | 515.9/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.9/4 |
| dewey-search | 515.9/4 |
| dewey-sort | 3515.9 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV001294829 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:26:34Z |
| institution | BVB |
| isbn | 3764334134 0817634134 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000781072 |
| oclc_num | 242685916 |
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| physical | 270 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Chenkin, Gennadij M. Verfasser aut Andreotti-Grauert theory by integral formulas Gennadi M. Henkin ; Jürgen Leiterer Boston [u.a.] Birkhäuser 1988 270 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 74 Integraldarstellung (DE-588)4127585-8 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Integralformel (DE-588)4161910-9 gnd rswk-swf Cauchy-Riemannsche Differentialgleichungen (DE-588)4147397-8 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s Mehrere Variable (DE-588)4277015-4 s Cauchy-Riemannsche Differentialgleichungen (DE-588)4147397-8 s Integralformel (DE-588)4161910-9 s 1\p DE-604 Komplexe Mannigfaltigkeit (DE-588)4031996-9 s Integraldarstellung (DE-588)4127585-8 s DE-604 Leiterer, Jürgen 1945- Verfasser (DE-588)1047631776 aut Progress in mathematics 74 (DE-604)BV000004120 74 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000781072&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chenkin, Gennadij M. Leiterer, Jürgen 1945- Andreotti-Grauert theory by integral formulas Progress in mathematics Integraldarstellung (DE-588)4127585-8 gnd Mehrere Variable (DE-588)4277015-4 gnd Funktionentheorie (DE-588)4018935-1 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Integralformel (DE-588)4161910-9 gnd Cauchy-Riemannsche Differentialgleichungen (DE-588)4147397-8 gnd |
| subject_GND | (DE-588)4127585-8 (DE-588)4277015-4 (DE-588)4018935-1 (DE-588)4031996-9 (DE-588)4161910-9 (DE-588)4147397-8 |
| title | Andreotti-Grauert theory by integral formulas |
| title_auth | Andreotti-Grauert theory by integral formulas |
| title_exact_search | Andreotti-Grauert theory by integral formulas |
| title_full | Andreotti-Grauert theory by integral formulas Gennadi M. Henkin ; Jürgen Leiterer |
| title_fullStr | Andreotti-Grauert theory by integral formulas Gennadi M. Henkin ; Jürgen Leiterer |
| title_full_unstemmed | Andreotti-Grauert theory by integral formulas Gennadi M. Henkin ; Jürgen Leiterer |
| title_short | Andreotti-Grauert theory by integral formulas |
| title_sort | andreotti grauert theory by integral formulas |
| topic | Integraldarstellung (DE-588)4127585-8 gnd Mehrere Variable (DE-588)4277015-4 gnd Funktionentheorie (DE-588)4018935-1 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Integralformel (DE-588)4161910-9 gnd Cauchy-Riemannsche Differentialgleichungen (DE-588)4147397-8 gnd |
| topic_facet | Integraldarstellung Mehrere Variable Funktionentheorie Komplexe Mannigfaltigkeit Integralformel Cauchy-Riemannsche Differentialgleichungen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000781072&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT chenkingennadijm andreottigrauerttheorybyintegralformulas AT leitererjurgen andreottigrauerttheorybyintegralformulas |